Question

Solve the equation: \[\dfrac{3}{7} + x = \dfrac{{17}}{7}\]

Answer 1

Hint: We will first consider the given equation and as we have to solve the equation for \[x\], we will subtract \[\dfrac{3}{7}\] on both the sides of the equation and then simplify both left-hand and right-hand side of the equation and on the right-hand side we have to take the L.C.M. for simplification which will give us the required answer.

Complete step-by-step answer:
We will first consider the given equation that is \[\dfrac{3}{7} + x = \dfrac{{17}}{7}\]
The objective is to solve the given equation for \[x\].
Now, to simplify the equation we will subtract \[\dfrac{3}{7}\] on both the sides of the equation that is the left-hand side and right-hand side of the equation.
Thus, we get,
\[ \Rightarrow \dfrac{3}{7} + x - \dfrac{3}{7} = \dfrac{{17}}{7} - \dfrac{3}{7}\]
Now, we will further simplify the above equation to evaluate the value of \[x\] and on the right-hand side we have to take the L.C.M. between the numbers.
Thus, we get
\[
   \Rightarrow x = \dfrac{{17 - 3}}{7} \\
   \Rightarrow x = \dfrac{{14}}{7} \\
 \]
Now, we can further simplify the right-hand side of the equation and we get,
\[ \Rightarrow x = 2\]
We can also verify the value of \[x\] by substituting the obtained value in the given expression,
Thus, we get,
\[
   \Rightarrow \dfrac{3}{7} + 2\mathop = \limits^? \dfrac{{17}}{7} \\
   \Rightarrow \dfrac{{17}}{7} = \dfrac{{17}}{7} \\
 \]
Thus, we can conclude that the value of \[x\] on solving the equation is 2.

Note: We can also bring \[\dfrac{3}{7}\] from the left-hand side to the right-hand side of the equation and change the sign from positive to negative and subtract the numbers by taking the L.C.M. which work as an alternative method. As the given equation is a linear equation of first order, so we can directly solve it for the value of \[x\].